Q1
The condition for a unique solution of $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ is:
📝 SolutionA unique solution (intersecting lines) requires $\frac{a_1}{a_2} \ne \frac{b_1}{b_2}$.
Q2
If $x = 2, y = 3$ is a solution of $ax + by = 12$ and $a = 3$, then $b$ is:
📝 SolutionSubstitute: $3(2) + b(3) = 12$, so $6 + 3b = 12$, giving $3b = 6$ and $b = 2$.
Q3
The sum of two numbers is 20 and their difference is 4. The larger number is:
📝 SolutionLet the numbers be $x$ and $y$. $x + y = 20$ and $x - y = 4$. Adding: $2x = 24$, so $x = 12$ (the larger).
Q4
Assertion (A): The equations $3x + 2y = 5$ and $6x + 4y = 9$ have no solution.
Reason (R): For parallel lines $\frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \frac{c_1}{c_2}$.
Choose the correct option:
Reason (R): For parallel lines $\frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \frac{c_1}{c_2}$.
Choose the correct option:
📝 SolutionRatios: $\frac{3}{6} = \frac{2}{4} = \frac{1}{2}$ but $\frac{5}{9} \ne \frac{1}{2}$. So the lines are parallel with no solution. R states this exact condition and explains A.
Q5
A pair of linear equations is inconsistent if it has:
📝 SolutionAn inconsistent pair has no solution, corresponding to parallel lines that never intersect.
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Class 10 · Maths
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